{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261103-r03-infinite-series-0002", "pilot_number": "R0034-17727", "number": 17727, "family_id": "qf-mod34-series-partial-sum", "title": { "zh-Hant": "第 17727 題：無窮級數", "en": "Question 17727: A Finite Partial Sum Is Not an Infinite-Series Limit" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261103-r03-infinite-series-0002", "batch_id": "batch-20261014-advance-20261103-r03-infinite-series-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-infinite-series" ], "title_zh": "無窮級數", "stem_zh": "固定index convention的partial-sum sequence與exact tail。操作=series-partial-sum；資料={\"terms\":[[1,3],[-1,4]]}。請依 [terms,partial_sum,count,boundary] 欄序回答。", "answer": { "kind": "expression", "value": "([1/3, -1/4], 1/12, 2, finite_partial_sum_only)", "explanation_zh": "Wave5第三層核對=([1/3, -1/4], 1/12, 2, finite_partial_sum_only)；依完整明示資料重算；geometric要求絕對ratio小於1且telescoping保留remainder；項趨零必要但不充分；長有限prefix不證收斂。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "無窮級數" ] }, "variant": { "family_id": "qf-mod34-series-partial-sum", "seed": 202611033002, "parameters": { "terms": [ [ 1, 3 ], [ -1, 4 ] ], "domain": "Exact_symbolic_series_certificate", "operation": "series-partial-sum", "semantic_template": "qf-mod34-series-partial-sum/{\"terms\":[[1,3],[-1,4]]}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_or_symbolic_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-14", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261014-advance-20261103-r03-infinite-series-0002", "batch_id": "batch-20261014-advance-20261103-r03-infinite-series-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "3db1a91af951a04759d19411366dc890e98bef2b4385b1099389b7a74c3d3c2b", "family_id": "qf-mod34-series-partial-sum", "seed": 202611033002, "semantic_template": "qf-mod34-series-partial-sum/{\"terms\":[[1,3],[-1,4]]}" }, "fields": { "title": "A Finite Partial Sum Is Not an Infinite-Series Limit", "stem": "Use the ordered explicit rational terms=[1/3, -1/4]. Give (terms,partial_sum,count,finite_partial_sum_only), reducing the supplied term values and computed finite sum exactly.", "answer": { "kind": "expression", "value": "([1/3, -1/4], 1/12, 2, finite_partial_sum_only)", "explanation": "Add only these listed terms with exact rational arithmetic. An empty list has sum zero. This finite operation supplies no conclusion about an unspecified continuation of the series. The exact result, retaining the requested order, is ([1/3, -1/4], 1/12, 2, finite_partial_sum_only)." }, "skills": [ "A Finite Partial Sum Is Not an Infinite-Series Limit" ], "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review." } }, "givens": [ { "id": "G001", "text": { "zh-Hant": "固定index convention的partial-sum sequence與exact tail。操作=series-partial-sum；資料={\"terms\":[[1,3],[-1,4]]}。請依 [terms,partial_sum,count,boundary] 欄序回答。", "en": "Use the ordered explicit rational terms=[1/3, -1/4]. Give (terms,partial_sum,count,finite_partial_sum_only), reducing the supplied term values and computed finite sum exactly." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "ordered finite series partial sum := sum(1/3, -1/4)", "after": "ordered finite series partial sum = 1/12", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 ordered finite series partial sum，不以小數近似替代。", "en": "Recompute ordered finite series partial sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/3", "-1/4" ], "output": "1/12", "label": "ordered finite series partial sum" } }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "original ordered reduced terms=[1/3, -1/4];term count=2", "after": "exact FINITE sum=1/12;finite_partial_sum_only", "relation": "implies", "rule_id": "series_finite_terms_no_unspecified_infinite_continuation", "conditions": [], "explanation": { "zh-Hant": "只加題目列出的項，空表和為0；沒有未知後續項的資訊，不能叫它無窮級數和。", "en": "Sum only the listed terms;the empty list has sum0.No unspecified continuation has been supplied,so this is not an infinite-series sum." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null } ], "math_model": { "result": [ [ "1/3", "-1/4" ], "1/12", 2, "finite_partial_sum_only" ] }, "conclusion": { "canonical_value": "([1/3, -1/4], 1/12, 2, finite_partial_sum_only)", "explanation": { "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。", "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged." } }, "definition_note": { "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。", "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate." }, "source": { "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db", "question_binding": { "batch_id": "batch-20261014-advance-20261103-r03-infinite-series-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261103-r03-infinite-series-foundations/questions.jsonl", "batch_sha256": "312c02ec0cfac82c5f3d25ced63c9d3a9b9b58bd4a3fae40456906f9b2dab03c", "original_line": 2, "original_line_sha256": "8d3d14e2c1e149596e4c10b9c69b0b855c107f7ddddf270c2f53da1d02da9205", "question_compact_sha256": "3db1a91af951a04759d19411366dc890e98bef2b4385b1099389b7a74c3d3c2b", "english_row_compact_sha256": "bff98967251fc031067179e50ca905af26578b806686c1350d58da3f4274983a", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261103-r03-infinite-series-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261103-r03-infinite-series-foundations.en.jsonl" }, "mko_bindings": { "mko-infinite-series": { "sha256": "f2c97043e047957807c3f303d9bf37bbe3d188f1721ae0dcfbab1537a45b8d0b", "english_sha256": "d540bafe796e5c209c969a5f34c55ef21c4244a2805d9558a5cbc8938ef09592", "original_path": "public/data/mko/infinite-series.json", "english_path": "public/data/i18n/editions/mko-infinite-series.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "d5b0037cbaeef26e3828d04bf29e0e0f6e466926098b6b09e3237d1fdbdbd0e2", "original_candidate_sha256": "f8d3541920637d0b83590a5534953597d341ad46a0dc5eff0743b74c56da91b8", "original_candidate_line_sha256": "f8d3541920637d0b83590a5534953597d341ad46a0dc5eff0743b74c56da91b8" }, "historical_source_state": { "review_state": { "derivation": "candidate_authored_and_locally_checked", "source_question_state": "candidate", "independent_AI_or_human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN" }, "scope_note": { "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。", "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged." }, "label": "Frozen producer metadata; current per-question review is separate below." }, "revision": { "id": "review-20261026-008-p35", "review_date": "2026-10-26", "owner_authorized_reader_publication": true, "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.", "review_receipts": { "semantic_review_sha256": "f73d099ebe3ff1c69a5d96f08c75b11b9e5b05120af40cf3ef388fce3b5c5336", "question_first_witness_sha256": "22675ffb6209b4fea076032b29b96e3dc19aad4244c54493f5f65f5e5d875699" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 2, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "854bcbc561548b4745517fd9eeead158ad725dae88fece9a1704a04f198b12ed", "arithmetic_steps": 1 }, "uses_answer_as_premise": false, "human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN", "Canonical_truth_promotion": false, "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged." } }